Basic Concepts of Geometry

a₁ Aabc ab/c abcd affine geometry angle sum automorphism b₁ basic c₁ Chapter collinear congruent convex quadrilateral convex set coplanar COROLLARY corresponding definition diagram disjoint distinct and noncollinear distinct points dyads element elliptic geometry endpoint equal equidistant equivalent Euclid's parallel postulate Euclidean geometry exactly Exercise exists a triangle exterior Exterior Angle Theorem FIGURE given line half-space Hence hypothesis I(Laob implies incidence geometry interior angles intersection intuitive isomorphic Labc Laob Lapb Ldef Lemma line contains linear Lobachevskian geometry Lobachevskian parallel mathematical midpoint neutral geometry non-Euclidean geometries O-segment oa ob oc oa)b opposite sides pair parallel lines parallel property perpendicular bisector planar Proof Prove Q(abcd real number rectangle relation representation right angle Saccheri quadrilateral satisfy separation set of points side of oa Similarly Suppose Theorem Theory of Incidence transverse unique xy meets